A nonvolatile memory cell according to the present invention comprises a bottom conductor, a semiconductor pillar, and a top conductor. The semiconductor pillar comprises a junction diode, including a bottom heavily doped region, a middle intrinsic or lightly doped region, and a top heavily doped region, wherein the conductivity types of the top and bottom heavily doped region are opposite. The junction diode is vertically oriented and is of reduced height, between about 500 angstroms and about 3500 angstroms. A monolithic three dimensional memory array of such cells can be formed comprising multiple memory levels, the levels monolithically formed above one another.